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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#941

Post by erichocean »

MelonUsk wrote: post #876
tim333 wrote: post #866

It reminds me of Frédéric Bastiat's Candle Makers' Petition. It satirised protectionism in the 1800s: >We candlemakers are suffering from the unfair competition of a foreign rival. This for­eign manufacturer of light has such an advantage over us that he floods our domestic markets with his product. And he offers it at a fantastically low price. The moment this foreigner appears in our country, all our customers de­s…

This is a straw men argument The petition is about a much broader problem: if we’ll demotivate people from understanding math, vibe math in a rush without making it understandable - math becomes useless Basically with pic generation at least we all understand what is on a pic - some cat or something With math it is trivial to generate a lot of stuff that is half-assed and just gives a plain yes/no but doesn’t get abs…

> vibe math

Ah yes, Lean 4. Famous for how unreliable it is. Absolute slop!

Re: A misalignment of AI in mathematics

#942

Post by erichocean »

cagz wrote: post #927

I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".

They want the AI labs to stop solving "important" math problems so that humans can do it, on the theory that when AI solves "important" math problems, it robs humans of the opportunity to gain new insights into those problems.

Total horse shit, but that's the essence of it.

Re: A misalignment of AI in mathematics

#943

Post by bharatsuthar »

socketcluster wrote: post #812

As a software engineer, 6 months ago. I was better than AI in essentially every way except raw typing speed. Now AI has surpassed me in fine-grained problem-solving ability. It can write more reliable code than I can, faster than I can, provided it is given the right guidance. But one thing that I'm still much better at is identifying technical opportunities and choosing the right tradeoffs. My feeling is that fronti…

Thanks for putting it in words. I feel the same about SOTA coding models. I get visibly frustrated by this and often find myself using curse words at Astra.

You're right it's very unhuman to miss obvious opportunities you mentioned. And what's why I think these models would continue sucking as long as they don't have human level general intelligence. They may get marginally better at these tasks but I don't think we can expect them to connect dots like humans before AGI.

Re: A misalignment of AI in mathematics

#944

Post by anyonecancode »

It sounds similar to the more thoughtful critiques of AI in programming. Treating AI as a lines of code (LOC) generator, where actual human beings end up not engaging with the domain the software is working in, and there is then little to no understanding or care to understand the resulting code, we call "slop." The term slop is definitely pejorative, but since most software is commercial, it ends up raising questions as to how much quality and domain knowledge matter if the goal is primarily marketplace success. Then we get those thorny questions of what is software for, anyway -- do we really accept the premise that "marketplace success" is the best, and perhaps only relevant, criteria?

The declaration here, as I understand it, is taking the premise that the point of mathematics _is_ the domain knowledge, and that using "solves math problems" as a benchmark is exactly the kind of shallow, domain-eroding approach to AI that in software we label "slop."

Re: A misalignment of AI in mathematics

#945

Post by bayindirh »

dgreensp wrote: post #925
GPerson wrote: post #710

Earlier quoted context omitted.

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

The declaration literally opens by writing that AI companies (or really anybody) saying, “Hey, let’s see if this powerful reasoning engine can solve an open problem in mathematics” is “detrimental” to the “science” of mathematics. Full stop. So I don’t think it’s being misrepresented. If it’s a science, why isn’t progress good in itself? You can’t have it both ways. The online comments I’ve read that side with the le…

Mathematics sits in a very different place w.r.t. other sciences. First of all, it's very meta. Yes, it can describe any phenomenon on our planet. On the other hand, advanced mathematics is a high mountain which is very hard to climb, and changes the climber in various and irreversible ways once the journey begins.

That's said, I'm a non-mathematician, but a computer scientist. Mathematics was always my weak part, because solving problems which doesn't mean anything doesn't motivate me, and when I'm not motivated, I fail.

Without digressing so much, I want to say that, some of the things in mathematics and mathematics adjacent sciences baffle me. Many mathematicians don't understand the proofs of others, yet they accept it since it checks out within the rules of mathematics. Moreover, many engineers don't understand the formulae they work with. I have developed a very performant Boundary Element Method evaluator, yet I don't know the reason of taking Gaussian Integrals over the surface. The only answer I got is "because the method works that way".

So, if computers can make the proofs now, and we have no curious students pecking their professors to understand how these works, the whole mathematics as a science could wither and die. Because besides it being a sport, it's the very language which can model and explain anything, but it's very hard to master and understand due to that nature.

Our professors warned us against using too much Mathematica, to make us learn things the hard way and make the knowledge permanent. Now, if we offload science to a matmul engine, it's possible that we lose the connection and never able to close the gap in some cases.

Again, it boils down to "This machine has no brain, use yours (or lose it)".

Re: A misalignment of AI in mathematics

#946

Post by reasonableklout »

munksbeer wrote: post #852
pvab3 wrote: post #668

Earlier quoted context omitted.

that is incredibly depressing

I feel the opposite. Human history is depressing overall. I imagine AI will eventually lead to less scarcity and better lives overall.

I am sure it will lead to more material wealth, but I can’t help but feel pessimistic about the political economy of making millions of people redundant. What leverage will knowledge workers have in the new world?

Re: A misalignment of AI in mathematics

#947

Post by jrowen »

NateEag wrote: post #772
jrowen wrote: post #248

This kinda reminds me of the documentary about the top Go master that got beaten by a computer in dramatic fashion and had an existential crisis. Man confronting his own limitations in the realm he previously ruled unchallenged, what a time to be alive. Nobody is going to care that the math isn't being done in the traditional way. The results speak for themselves, this is now a part of the landscape. No amount of han…

> No amount of hand-wringing is going to put the cat back in the bag. Adapt or perish. We can and have put some ugly, hissing, spitting cats into bags, some of which weren't even in one to begin with: * Chattel slavery is illegal, and the vast, vast majority of humans agree it's appalling it ever wasn't. * Food manufacturers in the US are no longer allowed to put highly-dangerous additives to their products and hide…

Thank you for this response, and I will clarify. I would roughly lump all of those into "social issues," whereas I would put "using AI to advance math" under "technological progress." That's why one article likened it to Socrates's fear of the written word. In broad strokes, I would say that once a technology becomes available, no amount of social pressure will stop it from proliferating.

If there's a distinction being made between "using AI for math" and "the particular methods being employed by OpenAI", I think that's splitting hairs. The core of the issue is that math is being done outside of people's heads by a different thinking system and they're worried about the implications.

If you look at something like the EPA (or the FDA as you mention), it is true that certain uses and side-effects of technology have been identified to be detrimental to society and have been restricted, but this letter doesn't seem to be in that league, it really seems like sour grapes to me. Dumping toxic chemicals into the water table is one thing, saying "we don't think people will learn from these methods in the same way that they traditionally have" doesn't hold as much water to me.

Re: A misalignment of AI in mathematics

#948

Post by YeGoblynQueenne »

grey-area wrote: post #837
YeGoblynQueenne wrote: post #835

Earlier quoted context omitted.

>> I’m no big AI cheerleader, but why don’t you try these models to see what they offer - they might suggest some things you haven’t thought of, or save you some time in your research. One reason not to try is to create an air gap between the OP's ideas and the data that future models can train on. We saw that the mathematicians who trusted OpenAI and Anthropic with their preliminary work found the rug pulled out of…

Unless you’re very weak-willed, I wouldn’t worry about independence. LLMs make mistakes all the time, they are nothing like an all-knowing oracle nor are they going to replace humans despite the absurd fantasies of LLM fans and those with a vested interest. Plagiarism is an interesting point, though honestly I think it would be fairly easy to work out who had published similar research if the LLM gives you an idea -…

Thanks. Regarding plagiarism, I agree that it is possible to check; I don't know how easy it is. But I do note that the mathematicians who complained that their work was plagiarised by AI did not seem to realise that they, themselves, were using a plagiarism machine and were instead quite comfortable admitting that, yeah, we worked our Euler result out together with Sol, Claude and the gang.

To clarify, they do attribute the original ideas to Cordoba and Martinez-Zoroa, but they don't seem to acknowledge that their result which they say was achieved "with a great deal of help from LLMs" is also derivative of others' work.

Independence is about avoiding making errors because of the influence of error-prone models. I guess I didn't explain it well.

Re: A misalignment of AI in mathematics

#949

Post by dsjoerg »

sweezyjeezy wrote: post #601
senfiaj wrote: post #272

Earlier quoted context omitted.

Well, chess is a sport where humans are supposed to compete. But math, programming, science are mostly not, and AI might affect economy, careers, etc.

As a chess fan, 100% this. We have known for the last ~15 years who the best human chess player is, and that he will lose against stockfish on his phone. But chess survives because of the human characters involved, the rivalries and dramas, watching two people trying to overcome each other under insane pressure, and sometimes coming up with something astonishing. In short - it's a sport. There is no equivalent in mat…

Uh I was literally on math team

Re: A misalignment of AI in mathematics

#950

Post by kaffekaka »

erichocean wrote: post #942
cagz wrote: post #927

I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".

They want the AI labs to stop solving "important" math problems so that humans can do it, on the theory that when AI solves "important" math problems, it robs humans of the opportunity to gain new insights into those problems. Total horse shit, but that's the essence of it.

The issue is that now that Navier-Stokes is "solved", the amount of resources put into researching it will be reduced, meaning that the insights and knowledge that would have come out of even failed attempts will never be.

An "unsolved problem" as a beacon to strive towards, gaining understanding along the way. With the beacon dead, noone will strive.

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